RTk mixed finite elements for some nonlinear problems.

Robert Eymard (1) , Thierry Gallouët (2) , Raphaèle Herbin (2)

1 LAMA - Laboratoire d'Analyse et de Mathématiques Appliquées
2 I2M - Institut de Mathématiques de Marseille

We show that the discrete operators and spaces of gradient discretizations can be designed so that the corresponding gradient scheme for a linear diffusion problem be identical to the Raviart–Thomas RT k mixed finite element method for both the primal mixed finite element formulation and the hybrid dual formulation. We then give the hybrid dual RT 0 scheme for the approximation of a nonlinear model for two-phase flow in porous media; its convergence is then known thanks to a recent proof of the convergence of gradient schemes for this problem.

Mots clés: gradient schemes; two phase flow; mixed finite element

Domaines: Analyse numérique [math.NA]

Robert Eymard, Thierry Gallouët, Raphaèle Herbin. RTk mixed finite elements for some nonlinear problems. . Mathematics and Computers in Simulation, 2014, pp.1-20. ⟨10.1016/j.matcom.2014.11.013⟩. ⟨hal-01127963⟩